Arbitrarily long factorizations in mapping class groups

2015-05-12
On a compact oriented surface of genus g with n ≥ 1 boundary components, δ1, δ2, ..., δn, we consider positive factorizations of the boundary multitwist tδ1 tδ2 ...tδn, where tδi is the positive Dehn twist about the boundary δi. We prove that for g ≥ 3, the boundary multitwist tδ1 tδ2 can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn-Morris, who proved this result for g ≥ 8. This fact has immediate corollaries on the Euler characteristics of the Stein fillings of conctact three manifolds.

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Citation Formats
M. Korkmaz, “Arbitrarily long factorizations in mapping class groups,” presented at the 49th Spring Topology and Dynamics Conference 2015 (14-16 May 2015), Bowling Green State University Bowling Green, OH, USA, 2015, Accessed: 00, 2021. [Online]. Available: http://at.yorku.ca/c/b/k/j/81.htm.